Algebra

Question

The sum of two whole number is 45 and their difference is less than 10. What will be the number of all possible pairs?

Answer 1

x+y = 45           ..(i)

|x-y| < 10              ..(ii)

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case 1: if x is larger (x>y)

(x-y) < 10              ..(iii)

solve (i) & (iii) ==> x < 27.5 & y > 17.5 & x > y

so, all posible whole no. pair (x,y)===> (27,18) , (26,19) , (25,20) , (24,21) , (23,22) 

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case 2 : if y is larger (x<y)

(y-x) < 10             ..(iv)

solve (i) & (iv) ==> x>17.5 & y<27.5 & x < y

so, all posible whole no. pair (x,y)===> (18,27) , (19,26) ,  (20,25)  , (21,24) , (22,23)

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Thus, total number of possible pair for (x,y) =10.

Answer 2

The number of possible pairs will be 5

(18,27) (19,26) (20,25) (21,24) (22,23)

Comments

should we count reversed pair also?

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I think yes we need to consider the reverse pairs also since x and y are different variables.So it should be 10.Please verify.

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@  Bhagyashree yes both cases should be considered. (x>y) & (x<y)